Lecture Notes: Introduction to Significant Figures and Basic Algebra
Introduction
Purpose: Introduction to significant figures and basic algebra for upcoming labs and throughout the course.
Importance of Measurements: Essential in science to connect, learn, and answer questions about the world.
Significant Figures
Definition and Importance
Significant figures determine which digits in a measurement are real and reliable.
Instruments vary in precision (e.g., scales measure to different decimal places).
Rules for Identifying Significant Figures
Non-Zero Numbers: Always significant.
Zeros Between Significant Figures: Significant (e.g., 701 has 3 significant figures).
Leading Zeros: Not significant (e.g., in 0.01, only the '1' is significant).
Trailing Zeros in Decimals: Significant if they follow a non-zero digit and a decimal point (e.g., 0.010 has 2 significant figures).
Exact Numbers: Counted numbers have no uncertainty (e.g., 95 students).
Calculations with Significant Figures
Addition/Subtraction: Align decimal points, result should match the smallest number of decimal places.
Multiplication/Division: Result should match the number with the fewest significant figures.
Algebra Fundamentals
Importance
Algebra is crucial for scientific calculations and solving unknowns (e.g., pH levels, bicarbonate concentration).
Order of Operations
Parentheses
Exponents
Multiplication/Division
Addition/Subtraction
Solving Equations
Isolate the variable by performing operations equally on both sides of the equation.
Example: Solve for X in simple and slightly complex equations.
Scientific Notation
Purpose
Used for expressing very large or small numbers efficiently (e.g., weights of cells, measurements in nanometers).
Converting to Scientific Notation
Large Numbers: Move decimal right to create a positive exponent.
Small Numbers: Move decimal left resulting in a negative exponent.
General Form: A number (1-9) followed by decimals multiplied by 10 to the power of N (positive or negative based on size).
Examples
Large and small numbers converted to scientific notation.
Importance of matching significant figures when converting.
Practical Applications
Various examples of real-world and scientific scenarios requiring significant figures and scientific notation (e.g., bacteria count, light wavelengths).
Additional Notations
Use of 'E' in calculators to denote *10^n.
Conclusion
Next steps include learning conversions and the factor-label method in subsequent sessions.